Electrides are materials with electrons localized at interstitial regions of the crystal lattice that act as anions. These materials have been identified as promising candidates for a myriad of applications, including catalysis, electron emission, and superconductivity.
Despite the discovery of a variety of electride materials in the past decade, there isn't a general-purpose experimental characterization method that can directly and accurately identify an electride.
As such, the identification of known electrides has relied on indirect means (i.e., via experimental measurement of physical properties believed to be associated with the interstitial electrons) and descriptors obtained from computational electronic structure calculations.
However, there isn't a unified theoretical understanding that can establish a link between these physical properties and descriptors, while explaining why electrons are stabilized at the interstitial regions for all known electrides.

In this thesis, a theoretical framework for the origin of interstitial electrons in electrides is presented.
Applying this theory to prototypical systems demonstrates that this concept can explain electride-like behavior in not only inorganic electrides but also other classes of material, including high-pressure electrides, organic electrides, and more broadly, Farbe center defects and solvated electrons.
Based on this theory, using the electron localization function and charge density obtained by ab initio simulations, a descriptor is further developed, and an electride figure of merit that can predict the likelihood of a system being an electride is defined.
By applying this descriptor to approximately 52,000 materials in the Materials Project database, a list of inorganic electride candidates is obtained and ranked based on their electride figure of merit.
Using selected candidates from the screening result, electride-like behavior is shown to be tunable by doping and/or external isotropic strain, which is in good accordance with what is expected from the theory.

Among the highest-ranked electride candidates from the high-throughput screening, LaBr and chemically-related systems are studied in detail for their unusual magnetic properties. These materials are demonstrated to be exfoliable layered electrides with their monolayer counterparts possessing flat bands that are understood as a physical manifestation of the dice tight-binding model.
These flat bands induce rich magnetic properties that are shown to be controlled by external strain. Specifically, for monolayer LaBr, under the effect of 2% biaxial tensile strain the magnetic ground state switches from antiferromagnetic where spins in the unit cell are anti-aligned to ferromagnetic where spins are fully aligned.
The origin of this magnetic phase transition is explained by the strain-dependent local magnetic moments. In the ferromagnetic phase, the local magnetic moments are much more sensitive to external strain than the antiferromagnetic phase. At under ~2% biaxial tensile strain, a much stronger spin-splitting in the ferromagnetic phase lowers the on-site Coulomb repulsion energies and causes the magnetic phase transition.

The results presented in this thesis suggest that electride-like behavior may not be as rare as previously perceived, and provide a database and a rational means for prioritizing future research of exotic electride materials such as strongly correlated electrides.